Problem: Solve for $x$ : $5\sqrt{x} + 7 = 8\sqrt{x} + 3$
Subtract $5\sqrt{x}$ from both sides: $(5\sqrt{x} + 7) - 5\sqrt{x} = (8\sqrt{x} + 3) - 5\sqrt{x}$ $7 = 3\sqrt{x} + 3$ Subtract $3$ from both sides: $7 - 3 = (3\sqrt{x} + 3) - 3$ $4 = 3\sqrt{x}$ Divide both sides by $3$ $\frac{4}{3} = \frac{3\sqrt{x}}{3}$ Simplify. $\dfrac{4}{3} = \sqrt{x}$ Square both sides. $\dfrac{4}{3} \cdot \dfrac{4}{3} = \sqrt{x} \cdot \sqrt{x}$ $x = \dfrac{16}{9}$